Foxiest of the Hounds

Alerting enemies doesn't mean "setting off an alarm". In fact, there are only a few missions where there are alarm systems which alert hostiles.

If you can hack and disable alarm systems in these missions, then you can actually alert enemies, but since the alarm systems are disabled, no alarm is ever sounded.

If you are interested in adopting a Maximum Stealth approach for this achievement/trophy, you can stack this with Pacifist as well.

Just remember that no weapon is completely silent (firing the tranquilizer rifle at one guard while under cover near a second may result in you hearing "was that a gunshot?" just before the second guard runs for an alarm).